The Cost of Arbitrariness for Individuals: Examining the Legal and Technical Challenges of Model Multiplicity

Model multiplicity, the phenomenon where multiple models achieve similar performance despite different underlying learned functions, introduces arbitrariness in model selection. While this arbitrariness may seem inconsequential in expectation, its impact on individuals can be severe. This paper explores various individual concerns stemming from multiplicity, including the effects of arbitrariness beyond final predictions, disparate arbitrariness for individuals belonging to protected groups, and the challenges associated with the arbitrariness of a single algorithmic system creating a monopoly across various contexts. It provides both an empirical examination of these concerns and a comprehensive analysis from the legal standpoint, addressing how these issues are perceived in the anti-discrimination law in Canada. We conclude the discussion with technical challenges in the current landscape of model multiplicity to meet legal requirements and the legal gap between current law and the implications of arbitrariness in model selection, highlighting relevant future research directions for both disciplines.